Networked dynamic systems with higher-order interactions: stability versus complexity.

The stability of complex systems is profoundly affected by underlying structures, which are often modeled as networks where nodes indicate system components and edges indicate pairwise interactions between nodes. However, such networks cannot encode the overall complexity of networked systems with higher-order interactions among more than two nodes. Set structures provide a natural description of pairwise and higher-order interactions where nodes are grouped into multiple sets based on their shared traits. Here we derive the stability criteria for networked systems with higher-order interactions by employing set structures. In particular, we provide a simple rule showing that the higher-order interactions play a double-sided role in community stability-networked systems with set structures are stabilized if the expected number of common sets for any two nodes is less than one. Moreover, although previous knowledge suggests that more interactions (i.e. complexity) destabilize networked systems, we report that, with higher-order interactions, networked systems can be stabilized by forming more local sets. Our findings are robust with respect to degree heterogeneous structures, diverse equilibrium states and interaction types.

Detecting Nonadditive Biotic Interactions and Assessing Their Biological Relevance among Temperate Rainforest Trees.

AbstractInteractions between and within abiotic and biotic processes generate nonadditive density-dependent effects on species performance that can vary in strength or direction across environments. If ignored, nonadditivities can lead to inaccurate predictions of species responses to environmental and compositional changes. While there are increasing empirical efforts to test the constancy of pairwise biotic interactions along environmental and compositional gradients, few assess both simultaneously. Using a nationwide forest inventory that spans broad ambient temperature and moisture gradients throughout New Zealand, we address this gap by analyzing the diameter growth of six focal tree species as a function of neighbor densities and climate, as well as neighbor × climate and neighbor × neighbor statistical interactions. The most complex model featuring all interaction terms had the highest predictive accuracy. Compared with climate variables, biotic interactions typically had stronger effects on diameter growth, especially when subjected to nonadditivities from local climatic conditions and the density of intermediary species. Furthermore, statistically strong (or weak) nonadditivities could be biologically irrelevant (or significant) depending on whether a species pair typically interacted under average or more extreme conditions. Our study highlights the importance of considering both the statistical potential and the biological relevance of nonadditive biotic interactions when assessing species performance under global change.

Food web context modifies predator foraging and weakens trophic interaction strength.

Trophic interaction modifications (TIM) are widespread in natural systems and occur when a third species indirectly alters the strength of a trophic interaction. Past studies have focused on documenting the existence and magnitude of TIMs; however, the underlying processes and long-term consequences remain elusive. To address this gap, we experimentally quantified the density-dependent effect of a third species on a predator's functional response. We conducted short-term experiments with ciliate communities composed of a predator, prey and non-consumable 'modifier' species. In both communities, increasing modifier density weakened the trophic interaction strength, due to a negative effect on the predator's space clearance rate. Simulated long-term dynamics indicate quantitative differences between models that account for TIMs or include only pairwise interactions. Our study demonstrates that TIMs are important to understand and predict community dynamics and highlights the need to move beyond focal species pairs to understand the consequences of species interactions in communities.

Identifying Diagnostic Biomarkers for Autism Spectrum Disorder From Higher-order Interactions Using the PED Algorithm.

In the field of neuroimaging, more studies of abnormalities in brain regions of the autism spectrum disorder (ASD) usually focused on two brain regions connected, and less on abnormalities of higher-order interactions of brain regions. To explore the complex relationships of brain regions, we used the partial entropy decomposition (PED) algorithm to capture higher-order interactions by computing the higher-order dependencies of all three brain regions (triads). We proposed a method for examining the effect of individual brain regions on triads based on the PED and surrogate tests. The key triads were discovered by analyzing the effects. Further, the hypergraph modularity maximization algorithm revealed the higher-order brain structures, of which the link between right thalamus and left thalamus in ASD was more loose compared with the typical control (TC). Redundant key triad (left cerebellum crus 1 and left precuneus and right inferior occipital gyrus) exhibited a discernible attenuation in interaction in ASD, while the synergistic key triad (right cerebellum crus 1 and left postcentral gyrus and left lingual gyrus) indicated a notable decline. The results of classification model further confirmed the potential of the key triads as diagnostic biomarkers.

The neuron mixer and its impact on human brain dynamics.

A signal mixer facilitates rich computation, which has been the building block of modern telecommunication. This frequency mixing produces new signals at the sum and difference frequencies of input signals, enabling powerful operations such as heterodyning and multiplexing. Here, we report that a neuron is a signal mixer. We found through ex vivo and in vivo whole-cell measurements that neurons mix exogenous (controlled) and endogenous (spontaneous) subthreshold membrane potential oscillations, producing new oscillation frequencies, and that neural mixing originates in voltage-gated ion channels. Furthermore, we demonstrate that mixing is evident in human brain activity and is associated with cognitive functions. We found that the human electroencephalogram displays distinct clusters of local and inter-region mixing and that conversion of the salient posterior alpha-beta oscillations into gamma-band oscillations regulates visual attention. Signal mixing may enable individual neurons to sculpt the spectrum of neural circuit oscillations and utilize them for computational operations.

HSH-UNet: Hybrid selective high order interactive U-shaped model for automated skin lesion segmentation.

The use of computer-assisted clinical dermatologists to diagnose skin diseases is an important aid. And computer-assisted techniques mainly use deep neural networks. Recently, the proposal of higher-order spatial interaction operations in deep neural networks has attracted a lot of attention. It has the advantages of both convolution and transformers, and additionally has the advantages of efficient, extensible and translation-equivariant. However, the selection of the interaction order in higher-order interaction operations requires tedious manual selection of a suitable interaction order. In this paper, a hybrid selective higher-order interaction U-shaped model HSH-UNet is proposed to solve the problem that requires manual selection of the order. Specifically, we design a hybrid selective high-order interaction module HSHB embedded in the U-shaped model. The HSHB adaptively selects the appropriate order for the interaction operation channel-by-channel under the computationally obtained guiding features. The hybrid order interaction also solves the problem of fixed order of interaction at each level. We performed extensive experiments on three public skin lesion datasets and our own dataset to validate the effectiveness of our proposed method. The ablation experiments demonstrate the effectiveness of our hybrid selective higher order interaction module. The comparison with state-of-the-art methods also demonstrates the superiority of our proposed HSH-UNet performance. The code is available at https://github.com/wurenkai/HSH-UNet.

Master regulators of biological systems in higher dimensions.

A longstanding goal of biology is to identify the key genes and species that critically impact evolution, ecology, and health. Network analysis has revealed keystone species that regulate ecosystems and master regulators that regulate cellular genetic networks. Yet these studies have focused on pairwise biological interactions, which can be affected by the context of genetic background and other species present, generating higher-order interactions. The important regulators of higher-order interactions are unstudied. To address this, we applied a high-dimensional geometry approach that quantifies epistasis in a fitness landscape to ask how individual genes and species influence the interactions in the rest of the biological network. We then generated and also reanalyzed 5-dimensional datasets (two genetic, two microbiome). We identified key genes (e.g., the rbs locus and pykF) and species (e.g., Lactobacilli) that control the interactions of many other genes and species. These higher-order master regulators can induce or suppress evolutionary and ecological diversification by controlling the topography of the fitness landscape. Thus, we provide a method and mathematical justification for exploration of biological networks in higher dimensions.

Kernel-based joint independence tests for multivariate stationary and non-stationary time series.

Multivariate time-series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the accurate statistical modelling and analysis of such systems. Here, we introduce kernel-based statistical tests of joint independence in multivariate time series by extending the d-variable Hilbert-Schmidt independence criterion to encompass both stationary and non-stationary processes, thus allowing broader real-world applications. By leveraging resampling techniques tailored for both single- and multiple-realization time series, we show how the method robustly uncovers significant higher-order dependencies in synthetic examples, including frequency mixing data and logic gates, as well as real-world climate, neuroscience and socio-economic data. Our method adds to the mathematical toolbox for the analysis of multivariate time series and can aid in uncovering high-order interactions in data.

Opinion Dynamics with Higher-Order Bounded Confidence.

The higher-order interactions in complex systems are gaining attention. Extending the classic bounded confidence model where an agent's opinion update is the average opinion of its peers, this paper proposes a higher-order version of the bounded confidence model. Each agent organizes a group opinion discussion among its peers. Then, the discussion's result influences all participants' opinions. Since an agent is also the peer of its peers, the agent actually participates in multiple group discussions. We assume the agent's opinion update is the average over multiple group discussions. The opinion dynamics rules can be arbitrary in each discussion. In this work, we experiment with two discussion rules: centralized and decentralized. We show that the centralized rule is equivalent to the classic bounded confidence model. The decentralized rule, however, can promote opinion consensus. In need of modeling specific real-life scenarios, the higher-order bounded confidence is more convenient to combine with other higher-order interactions, from the contagion process to evolutionary dynamics.

Capturing complex interactions in disease ecology with simplicial sets.

Network approaches have revolutionized the study of ecological interactions. Social, movement and ecological networks have all been integral to studying infectious disease ecology. However, conventional (dyadic) network approaches are limited in their ability to capture higher-order interactions. We present simplicial sets as a tool that addresses this limitation. First, we explain what simplicial sets are. Second, we explain why their use would be beneficial in different subject areas. Third, we detail where these areas are: social, transmission, movement/spatial and ecological networks and when using them would help most in each context. To demonstrate their application, we develop a novel approach to identify how pathogens persist within a host population. Fourth, we provide an overview of how to use simplicial sets, highlighting specific metrics, generative models and software. Finally, we synthesize key research questions simplicial sets will help us answer and draw attention to methodological developments that will facilitate this.

Flickering Emergences: The Question of Locality in Information-Theoretic Approaches to Emergence.

"Emergence", the phenomenon where a complex system displays properties, behaviours, or dynamics not trivially reducible to its constituent elements, is one of the defining properties of complex systems. Recently, there has been a concerted effort to formally define emergence using the mathematical framework of information theory, which proposes that emergence can be understood in terms of how the states of wholes and parts collectively disclose information about the system's collective future. In this paper, we show how a common, foundational component of information-theoretic approaches to emergence implies an inherent instability to emergent properties, which we call flickering emergence. A system may, on average, display a meaningful emergent property (be it an informative coarse-graining, or higher-order synergy), but for particular configurations, that emergent property falls apart and becomes misinformative. We show existence proofs that flickering emergence occurs in two different frameworks (one based on coarse-graining and another based on multivariate information decomposition) and argue that any approach based on temporal mutual information will display it. Finally, we argue that flickering emergence should not be a disqualifying property of any model of emergence, but that it should be accounted for when attempting to theorize about how emergence relates to practical models of the natural world.

Non-additive biotic interactions improve predictions of tropical tree growth and impact community size structure.

Growth in individual size or biomass is a key demographic component in population models, with wide-ranging applications from quantifying species performance across abiotic or biotic conditions to assessing landscape-level dynamics under global change. In forest ecology, the responses of tree growth to biotic interactions are widely held to be crucial for understanding forest diversity, function, and structure. To date, most studies on plant-plant interactions only examine the additive competitive or facilitative interactions between species pairs; however, there is increasing evidence of non-additive, higher-order interactions (HOIs) impacting species demographic rates. When HOIs are present, the dynamics of a multispecies community cannot be fully understood or accurately predicted solely from pairwise outcomes because of how additional species "interfere" with the direct, pairwise interactions. Such HOIs should be particularly prevalent when species show non-linear functional responses to resource availability and resource-acquisition traits themselves are density dependent. With this in mind, we used data from a tropical secondary forest-a system that fulfills both of these conditions-to build an ontogenetic diameter growth model for individuals across 10 woody-plant species. We allowed both direct and indirect interactions within communities to influence the species-specific growth parameters in a generalized Lotka-Volterra model. Specifically, indirect interactions entered the model as higher-order quadratic terms, i.e., non-additive effects of conspecific and heterospecific neighbor size on the focal individual's growth. For the whole community and for four out of 10 focal species, the model that included HOIs had more statistical support than the model that included only direct interactions, despite the former containing a far greater number of parameters. HOIs had comparable effect sizes to direct interactions, and tended to further reduce the diameter growth rates of most species beyond what direct interactions had already reduced. In a simulation of successional stand dynamics, the inclusion of HOIs led to rank swaps in species' diameter hierarchies, even when community-level size distributions remained qualitatively similar. Our study highlights the implications, and discusses possible mechanisms, of non-additive density dependence in highly diverse and light-competitive tropical forests.

A framework and standardized terminology to facilitate the study of predation-risk effects.

The very presence of predators can strongly influence flexible prey traits such as behavior, morphology, life history, and physiology. In a rapidly growing body of literature representing diverse ecological systems, these trait (or "fear") responses have been shown to influence prey fitness components and density, and to have indirect effects on other species. However, this broad and exciting literature is burdened with inconsistent terminology that is likely hindering the development of inclusive frameworks and general advances in ecology. We examine the diverse terminology used in the literature, and discuss pros and cons of the many terms used. Common problems include the same term being used for different processes, and many different terms being used for the same process. To mitigate terminological barriers, we developed a conceptual framework that explicitly distinguishes the multiple predation-risk effects studied. These multiple effects, along with suggested standardized terminology, are risk-induced trait responses (i.e., effects on prey traits), interaction modifications (i.e., effects on prey-other-species interactions), nonconsumptive effects (i.e., effects on the fitness and density of the prey), and trait-mediated indirect effects (i.e., the effects on the fitness and density of other species). We apply the framework to three well studied systems to highlight how it can illuminate commonalities and differences among study systems. By clarifying and elucidating conceptually similar processes, the framework and standardized terminology can facilitate communication of insights and methodologies across systems and foster cross-disciplinary perspectives.

Indirect Effects Explain the Role of Parasites in Ecosystems.

Parasites are increasingly recognized as integral members of ecological communities, but their ecological effects remain less clear. Here, I propose that, to uncover the unique role of parasites, we must understand their indirect effects, which differ in important ways from those caused by predators. Similar to predators, parasites can cause density-mediated indirect effects (DMIEs) through their consumptive effects, and trait-mediated indirect effects (TMIEs) through their nonconsumptive effects; however, because they can consume a host without killing it, parasites can also trigger TMIEs through their consumptive effects. I consider the relative importance of each parasite-induced indirect interaction type and demonstrate their population-, community-, and ecosystem-level consequences. This paper contributes to recent efforts to unite predator-prey and parasite-host theory under a general consumer-resource framework.

Healthy but smaller herds: Predators reduce pathogen transmission in an amphibian assemblage.

Predators and pathogens are fundamental components of ecological communities that have the potential to influence each other via their interactions with victims and to initiate density- and trait-mediated effects, including trophic cascades. Despite this, experimental tests of the healthy herds hypothesis, wherein predators influence pathogen transmission, are rare. Moreover, no studies have separated effects mediated by density vs. traits. Using a semi-natural mesocosm experiment, we investigated the interactive effects of predatory dragonfly larvae (caged or lethal [free-ranging]) and a viral pathogen, ranavirus, on larval amphibians (grey treefrogs and northern leopard frogs). We determined the influence of predators on ranavirus transmission and the relative importance of density- and trait-mediated effects on observed patterns. Lethal predators reduced ranavirus infection prevalence by 57%-83% compared to no-predator and caged-predator treatments. The healthy herds effect was more strongly associated with reductions in tadpole density than behavioural responses to predators. We also assessed whether ranavirus altered the responses of tadpoles to predators. In the absence of virus, tadpoles reduced activity levels and developed deeper tails in the presence of predators. However, there was no evidence that virus presence or infection altered responses to predators. Finally, we compared the magnitude of trophic cascades initiated by individual and combined natural enemies. Lethal predators initiated a trophic cascade by reducing tadpole density, but caged predators and ranavirus did not. The absence of a virus-induced trophic cascade is ostensibly the consequence of limited virus-induced mortality and the ability of infected individuals to continue interacting within the community. Our results provide support for the healthy herds hypothesis in amphibian communities. We uniquely demonstrate that density-mediated effects of predators outweigh trait-mediated effects in driving this pattern. Moreover, this study was one of the first to directly compare trophic cascades caused by predators and pathogens. Our results underscore the importance of examining the interactions between predators and pathogens in ecology.

A kernel machine method for detecting higher order interactions in multimodal datasets: Application to schizophrenia.

BACKGROUND: Technological advances are enabling us to collect multimodal datasets at an increasing depth and resolution while with decreasing labors. Understanding complex interactions among multimodal datasets, however, is challenging. NEW METHOD: In this study, we tested the interaction effect of multimodal datasets using a novel method called the kernel machine for detecting higher order interactions among biologically relevant multimodal data. Using a semiparametric method on a reproducing kernel Hilbert space, we formulated the proposed method as a standard mixed-effects linear model and derived a score-based variance component statistic to test higher order interactions between multimodal datasets. RESULTS: The method was evaluated using extensive numerical simulation and real data from the Mind Clinical Imaging Consortium with both schizophrenia patients and healthy controls. Our method identified 13-triplets that included 6 gene-derived SNPs, 10 ROIs, and 6 gene-specific DNA methylations that are correlated with the changes in hippocampal volume, suggesting that these triplets may be important for explaining schizophrenia-related neurodegeneration. COMPARISON WITH EXISTING METHOD(S): The performance of the proposed method is compared with the following methods: test based on only first and first few principal components followed by multiple regression, and full principal component analysis regression, and the sequence kernel association test. CONCLUSIONS: With strong evidence (p-value ≤0.000001), the triplet (MAGI2, CRBLCrus1.L, FBXO28) is a significant biomarker for schizophrenia patients. This novel method can be applicable to the study of other disease processes, where multimodal data analysis is a common task.

A parasite's modification of host behavior reduces predation on its host.

Parasite modification of host behavior is common, and the literature is dominated by demonstrations of enhanced predation on parasitized prey resulting in transmission of parasites to their next host. We present a case in which predation on parasitized prey is reduced. Despite theoretical modeling suggesting that this phenomenon should be common, it has been reported in only a few host-parasite-predator systems. Using a system of gregarine endosymbionts in host mosquitoes, we designed experiments to compare the vulnerability of parasitized and unparasitized mosquito larvae to predation by obligate predatory mosquito larvae and then compared behavioral features known to change in the presence of predatory cues. We exposed Aedes triseriatus larvae to the parasite Ascogregarina barretti and the predator Toxohrynchites rutilus and assessed larval mortality rate under each treatment condition. Further, we assessed behavioral differences in larvae due to infection and predation stimuli by recording larvae and scoring behaviors and positions within microcosms. Infection with gregarines reduced cohort mortality in the presence of the predator, but the parasite did not affect mortality alone. Further, infection by parasites altered behavior such that infected hosts thrashed less frequently than uninfected hosts and were found more frequently on or in a refuge within the microcosm. By reducing predation on their host, gregarines may be acting as mutualists in the presence of predation on their hosts. These results illustrate a higher-order interaction, in which a relationship between a species pair (host-endosymbiont or predator-prey) is altered by the presence of a third species.

Structure of the human DNA-repair protein RAD52 containing surface mutations.

The Rad52 protein is a eukaryotic single-strand DNA-annealing protein that is involved in the homologous recombinational repair of DNA double-strand breaks. The isolated N-terminal half of the human RAD52 protein (RAD52(1-212)) forms an undecameric ring structure with a surface that is mostly positively charged. In the present study, it was found that RAD52(1-212) containing alanine mutations of the charged surface residues (Lys102, Lys133 and Glu202) is highly amenable to crystallization. The structure of the mutant RAD52(1-212) was solved at 2.4 Šresolution. The structure revealed an association between the symmetry-related RAD52(1-212) rings, in which a partially unfolded, C-terminal region of RAD52 extended into the DNA-binding groove of the neighbouring ring in the crystal. The alanine mutations probably reduced the surface entropy of the RAD52(1-212) ring and stabilized the ring-ring association observed in the crystal.

Can antibodies against flies alter malaria transmission in birds by changing vector behavior?

Transmission of insect-borne diseases is shaped by the interactions among parasites, vectors, and hosts. Any factor that alters movement of infected vectors from infected to uninfeced hosts will in turn alter pathogen spread. In this paper, we study one such pathogen-vector-host system, avian malaria in pigeons transmitted by fly ectoparasites, where both two-way and three-way interactions play a key role in shaping disease spread. Bird immune defenses against flies can decrease malaria prevalence by reducing fly residence time on infected birds or increase disease prevalence by enhancing fly movement and thus infection transmission. We develop a mathematical model that illustrates how these changes in vector behavior influence pathogen transmission and show that malaria prevalence is maximized at an intermediate level of defense avoidance by the flies. Understanding how host immune defenses indirectly alter disease transmission by influencing vector behavior has implications for reducing the transmission of human malaria and other vectored pathogens.